Properties and $N$-representability conditions of the two-body density matrix

TL;DR

This paper explores the properties of two-body reduced density matrices and derives necessary N-representability conditions to ensure they conform to quantum mechanical principles, aiding in many-electron system analysis.

Contribution

It introduces a comprehensive analysis of two-body density matrices and formulates new necessary N-representability conditions for many-electron quantum systems.

Findings

Derived necessary N-representability conditions.

Analyzed properties of two-body density matrices.

Linked wave functions to density matrix properties.

Abstract

A summary is presented of the properties of the coefficient matrices formed by expanding the two-body reduced density matrix in a complete set of two-electron wave functions. Calculating the relationship between the many electron wave function and these so-called two-body density matrices enables the derivation of necessary $N$-representability conditions that ensure a given matrix obeys the postulates of many-body quantum mechanics.